| HELICAL GEARING |
| To Obtain
|
From
Known |
Symbol
and Formula |
| Normal circular
pitch |
Transverse
circular pitch |
Pcn =
Pc cos y |
| Normal diametral
pitch |
Transverse
diametral pitch |
Pdn =
Pd
cos y |
| Axial pitch |
Circular pitches |
Pa = Pc
cot y = Pcn
sin
y |
| Normal pressure
angle |
Transverse
pressure angle |
tan fn = tan f cos y |
| Pitch diameter |
Number of teeth
and pitch |
D =
N = N
Pd
Pdn cos y |
Center distance
(parallel shafts) |
Number of teeth
and pitch |
C =
N1 + N2
2 Pdn
cos y |
Center distance
(crossed shafts) |
Number of teeth
and pitch |
C = 1
( N1 +
N2 )
2 Pdn
cos y1 cos y2 |
Shaft angle
(Crssed shafts) |
Helix angles of 2
mated gears |
q = y1 + y2 |
| Addendum |
Pitch; or outside
and pitch
diameters |
a = 0.5 ( Do
- D ) = 1
Pd |
| Dedendum |
Pitch diameter
and root
diameter (DR) |
b = 0.5 ( D - DR
) |
| Clearance |
Addendum and
dedendum |
c = b-a |
| Working depth |
Addendum |
hk =
2a |
Transverse
pressure
angle |
Base circle
diameter and
pitch circle diameter |
cos ft = Db / D |
| Pitch helix angle
|
Number of teeth,
normal diametral pitch and
pitch diameter |
cos y = N
Pn D |
| Lead |
Pitch diameter
and
pitch helix angle |
L = p D cos y |
| INVOLUTE
GEAR PAIRS |
| To Obtain |
Symbols |
Spur or
Helical Gears ( g gear; p = pinion) |
| Length of action |
ZA |
ZA =
(C² - (Rb+rb)²)½ (maximum)
ZA = (Ro²-Rb²)½
(ro²-rb²-C sin fr)½ |
| Start of active
profile |
SAP |
SAPp =
-(Ro²-Rb²)½
SAPg = Zmax-(ro²-rb²)½ |
| Contact ratio |
Rc |
Rcg = ((SAP)² +
Rb²)½; Rcp = ((SAP)² + rb²)½ |